Question

Solve for theta. cos ^2 theta -3 cos theta+2/sin ^2 theta =2​

Answer 1

sin^2 theta + cos theta = 2 (Use the Pythagorean identity sin^2 theta + cos^2 theta = 1 to replace sin^2 theta in the given equation).

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Answer 2

Step-by-step explanation:

Given, sin θ + 2cos θ = 1

Squaring on both sides, we get

Now, (sin θ + 2cos θ)2 = 12

=> sin2 θ + 4cos2 θ + 4*sin θ * cos θ = 1

=> 1 - cos2 θ + 4(1 - sin2 θ) + 4 * sin θ * cos θ = 1 [Since sin2 θ + cos2 θ = 1]

=> 1 - cos2 θ + 4 - 4 * sin2 θ + 4 * sin θ * cos θ = 1

=> 5 - cos2 θ - 4 * sin2 θ + 4 * sin θ * cos θ = 1

=> 5 - 1 = cos2 θ + 4 * sin2 θ - 4 * sin θ * cos θ

=> cos2 θ + 4 * sin2 θ - 4 * sin θ * cos θ = 4

=> 4 * sin2 θ + cos2 θ - 4 * sin θ * cos θ = 22

=> (2sin θ - cos θ)2 = 22

=> 2sin θ - cos θ = ±2

Hence proved